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Supporting Information for "Ecological emergence of thermal clines in body size"
Authored by Eric Edeline, Gérard Lacroix, Christine Delire, Nicolas Poulet, Stéphane Legendre
1. Temperature-dependent allometric scaling of net energy gain
Figure S1. Mass-specific energy gain rate (defined as I-M in Eq. S1) as a function of temperature in the
range 0-40ºC (273-313 K) for differently sized vertebrate ectotherms (a, c; dotted line: mc = 1g, dashed
line: mc = 10g, solid line: mc = 100g) and multicellular invertebrates (b, d; dotted line: mc = 0.01g,
dashed line: mc = 0.1g, solid line: mc = 1g) in which ingestion is either ecologically-limited (fI=0.2, a,
b) or physiologically-limited (fI=0.9, c; d). Other parameters are as follows: vertebrate ectotherms:
aI=6.4, aM=2.3, EI=0.67, EM=0.43; multicellular invertebrates: aI=9.7, aM=0.51, EI=0.77, EM=0.79.
Following Vasseur & McCann (2005) and references therein, we write the mass-specific biological rate
functions including body mass and temperature scaling as:
EI T −T
(
0
EM T − T
0
I=f I a I (T 0 )m−c 0. 25 e
M=a M (T 0 )m−c 0 . 25 e
(
)/ kTT 0
)/ kTT 0
Eq. S1,
where I is energy intake rate, M is the rate of energy loss to metabolism, mc is consumer body mass,
ai(T0) are empirically-derived intercepts of the allometric relationships (in kg (kg year)-1 kg0.25) which
represent the maximum sustainable rates (physiological maxima) measured at temperature T0, T is
absolute temperature (in K), k is Boltzmann's constant (8.618  10-5 eV K-1), Ea is activation energy (in
1
eV) of the reaction, and fI represents the realized fraction (in the wild) of the physiological ingestion
maxima that can be attained under ideal conditions. When species are “ecologically limited” for
ingestion fI << 1, while fI ≈ 1 when species are “physiologically-limited” for ingestion (Vasseur &
McCann, 2005). In Fig. S1, we posit mass-specific energy gain rate G = I-M (Ohlberger et al., 2011),
and represent G as a function of T for differently-sized vertebrate ectotherms (Figs. S1a and c) and
multicellular invertebrates (Figs. S1b and d) under either ecological (fI=0.2, Figs. S1a and b) or
physiological (fI=0.9, Figs. S1c and d) limitation for ingestion (other parameters are as follows:
vertebrate ectotherms: aI=6.4, aM=2.3, EI=0.67, EM=0.43; multicellular invertebrates: aI=9.7, aM=0.51,
EI=0.77, EM=0.79). In all cases, G increases with temperature, consistent with the general finding that
growth efficiency increases at higher temperatures (Angilletta & Dunham, 2003). However, the thermal
sensitivity of G is higher in smaller organisms, so that warming generates a competitive asymmetry in
favor of smaller organisms. Note that under “ecological limitation” and low temperatures, large
vertebrates are more competitive than small vertebrates as they starve less fast (Fig. S1a). Interestingly,
similar results were derived independently by Ohlberger et al. (2011) using more sophisticated data on
perch Perca fluvitatilis physiological rates, which incorporated a more realistic, hump-shaped
relationship between energy gain rate and temperature (i.e., temperature optimum). This suggests that,
although Arrhenius kinetics do not account for the hump-shaped nature of physiological and ecological
rates (Knies & Kingsolver, 2010), they still provide fairly good approximations (Dell et al., 2011).
2. Log-normal distributions for size-dependent niches
Hutchinson (Hutchinson, 1957) defined the ecological niche as the range of environmental conditions
that allow a population growth rate to be zero or positive. The niche can be though of as a n
dimensional volume with its n axes represented by requisite resources. MacArthur & Levins
(MacArthur & Levins, 1967) extend the theory by considering niche axes as "resource utilization" axes
(Schoener, 2009). Instead of describing population growth variation in response to environmental
variation, this resource-utilization niche describes the frequency distribution of resource use along each
niche axis and directly quantifies the intensity of competition from the overlap of resource utilization
niches (MacArthur & Levins, 1967; MacArthur, 1972) (Figure S2).
However, a major problem of the hypervolume approach is that its entire dimensionality generally
extends beyond the technical and practical abilities of any one researcher. One way to circumvent this
dimensionality problem is to collapse all resource axes onto one single, synthetic resource axis.
Particularly relevant to this unidimensional approach is the use of a consumer body size axis (Figure
S2). Indeed, body size correlates with prey size and type, ingestion rate, energy requirements, home
ranges, and encounter rates (Peters, 1983; Jetz et al., 2004; Brown et al., 2004; Woodward et al., 2005;
Brose, 2010; Lang et al., 2012). Hence, the strength of competition is proportional to the overlap of
body size distributions between competitors (MacArthur & Levins, 1967; MacArthur, 1972). On
macroevolutionary time scales, this size-dependent competition is predicted to result in character
displacement and in a more or less regular spacing of potential competitors along a body size gradient;
and in fact a number of examples support this prediction (Hutchinson, 1959; Pyke, 1982; Dayan et al.,
1989; Hermoyian et al., 2002). This size-dependent, unidimensional approach to resource utilization
niche can also be used to define the niche of predators for a focal species. Meta-analyses show that the
average body mass of a predator is 100 times the body mass of its prey (Brose et al., 2006), and the
predator's niche may thus correspond to the niche of competitors, right-translated by 100 units along a
body mass axis (or by 4.6 units along a body length axis since mass ≈ length3). We apply this
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framework to compute interactions strengths experienced by individual fish in communities. We
considered competition to be maximal between two individual competitors whose body size ratio is
equal to 1 (MacArthur & Levins, 1967; MacArthur, 1972), and predation to be maximal when the
predator/prey length ratio is equal to 4.6 (Brose et al., 2006).
Figure S2. Multidimensional resource utilization niches projected onto a single consumer body size
axis. From top to bottom, the decreasing overlap gradient between consumer size distributions
determines a decreasing gradient of competition strength.
Choice of the shape of the resource utilization niche around this maximum also requires some
discussions. The theory of resource utilization niches was developed assuming normal (Gaussian)
utilization curves (Figure S2, (MacArthur, 1972)). However, several authors stress that normal
utilization niches represent a case of limited generality (Roughgarden, 1974; Wilson, 1975; Abrams et
al., 2008; Pigolotti et al., 2010), and there seems to be no general rule for the shape of the utilization
distribution except that its variance should increase with its mean because prey-size range (niche
breath) increases with predator size (Wilson, 1975; Woodward et al., 2005). Here, we used a lognormal
resource utilization distribution because (i) body sizes are often log-normally distributed (such as in our
dataset), (ii) the variance of the log-normal distribution increases with its mean, accounting for the fact
that niche breadth increases with body size, and (iii) because of its heavy right tail the lognormal
distribution accounts for the fact that, within a niche, larger consumers have higher consumption rates
(Brown et al., 2004) and are thus likely to be stronger interactors than smaller consumers.
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3. Table S1. Fish species included in our analysis. Species-specific number of observations, trophic
guild, piscivory probability (based on diet data from Fishbase http://www.fishbase.org/) and mean body
length in our dataset (from a log-normal distribution). Generalists: macroinvertebrates and fish;
Insectivores: insects; Invertivores: insects, mollusks, and crustaceans; Omnivores: invertebrates and
plants; Piscivores: fish.
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Species latin name
Species common name
N
Trophic guild
Abramis brama
Alburnoides bipunctatus
Alburnus alburnus
Ameiurus melas
Anguilla anguilla
Aspius aspius
Barbus barbus
Barbus meridionalis
Blicca bjoerkna
Carassius sp.
Chondrostoma nasus
Chondrostoma toxostoma
Cobitis taenia
Cottus sp.
Cottus petiti
Cyprinus carpio
Esox lucius
Gambusia holbrooki
Gasterosteus aculeatus
Gobio sp.
Gymnocephalus cernuus
Lampetra fluviatilis
Lampetra planeri
Lepomis gibbosus
Leucaspius delineatus
Leuciscus burdigalensis
Leuciscus cephalus
Leuciscus idus
Leuciscus leuciscus
Lota lota
Micropterus salmoides
Misgurnus fossilis
Barbatula barbatula
Onchorhynchus mykiss
Pachychilon pictus
Perca fluviatilis
Phoxinus phoxinus
Pseudorasbora parva
Pungitius pungitius
Rhodeus amarus
Rutilus rutilus
Salaria fluviatilis
Salmo salar
Salmo trutta
Salvelinus fontinalis
Scardinius erythrophtalmus
Silurus glanis
Sander lucioperca
Telestes souffia
Thymallus thymallus
Tinca tinca
Zingel asper
Freshwater bream
Schneider
Bleak
Black bullhead
Eel
Asp
Barbel
Mediterranean barbel
White bream
Crucian carp
Common nase
French nase
Spined loach
Sculpin
Lez sculpin
Common carp
Pike
Mosquitofish
Threespined stickleback
Gudgeon
Ruffe
River lamprey
European brook lamprey
Pumpkinseed
Sunbleak
Rostrum dace
Chub
Orfe
Common dace
Burbot
Largemouth bass
Weatherfish
Stone loach
Rainbow trout
Albanian Roach
Perch
Eurasian minnow
Topmouth gudgeon
Ninespined stickleback
Bitterling
Roach
Freshwater blenny
Atlantic salmon
Brown trout
Brook trout
Rudd
Wels catfish
Pikeperch
Vairone
Grayling
Tench
Rhone streber
23,784
75,138
128,108
14,975
180,444
383
125,293
23,796
33,532
5,924
29,862
17,469
4,699
269,207
1,232
5,804
23,061
1,603
18,828
390,104
9,267
86
45,423
45,725
2,181
418
419,627
208
78,193
4,963
1,459
1,961
281,339
3,813
1,815
87,796
367,104
9,323
16,234
39,369
356,333
1,217
56,089
846,862
412
16,527
6,149
3,640
58,847
9,419
16,530
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Generalist
Omnivore
Insectivore
Generalist
Generalist
Piscivore
Generalist
Omnivore
Omnivore
Omnivore
Omnivore
Omnivore
Omnivore
Generalist
Omnivore
Generalist
Piscivore
Insectivore
Invertivore
Omnivore
Generalist
Piscivore
Omnivore
Generalist
Insectivore
Insectivore
Generalist
Generalist
Insectivore
Piscivore
Piscivore
Omnivore
Omnivore
Generalist
Generalist
Piscivore
Omnivore
Generalist
Invertivore
Insectivore
Omnivore
Omnivore
Generalist
Generalist
Generalist
Omnivore
Generalist
Piscivore
Omnivore
Generalist
Invertivore
Omnivore
Piscivory
probability 
0.5
0
0
1
1
1
1
0
0
0
0
0
0
1
0
0.5
1
0
0
0
1
1
0
1
0
0
1
0.5
0
1
1
0
0
1
0.5
1
0
0.5
0
0
0
0
1
1
1
0
1
1
0
0.5
0
0
Mean body
length (mm)
173.8
73.5
73.1
135.3
359.3
106.8
164.2
115.5
110.6
173.4
229.0
134.1
76.4
64.3
33.4
286.3
271.9
29.6
41.6
88.8
93.9
122.9
119.8
80.0
45.7
159.9
160.0
98.1
134.9
244.3
115.7
140.8
69.5
217.1
91.9
124.8
55.4
58.4
37.7
46.7
120.9
63.3
103.0
144.2
202.8
108.5
285.3
222.3
101.8
201.3
160.2
121.6
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